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4.6 isosceles and equilateral triangles ink.notebook · 4.6 isosceles and equilateral triangles...

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4.6 isosceles and equilateral triangles ink.notebook 1 November 06, 2017 Page 151 4.6 Isosceles and Equilateral Triangles Page 152 Page 153 Lesson Objectives Standards Lesson Notes Press the tabs to view details. 4.6 Isosceles and Equilateral Triangles
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  • 4.6isoscelesandequilateraltrianglesink.notebook

    1

    November06,2017

    Page 151

    4.6 Isosceles and Equilateral Triangles

    Page 152

    Page 153

    LessonObjectives Standards LessonNotes

    Pressthetabstoviewdetails.

    4.6 Isosceles and Equilateral Triangles

  • 4.6isoscelesandequilateraltrianglesink.notebook

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    LessonObjectives

    Pressthetabstoviewdetails.

    LessonNotesStandards

    Afterthislesson,youshouldbeabletosuccessfullyusetheoremaboutisoscelesandequilateraltrianglestofindmissingpartsoftriangles.

    LessonObjectives Standards LessonNotes

    G.SRT.5Usecongruenceandsimilaritycriteriafortrianglestosolveproblemsandtoproverelationshipsingeometricfigures.G.CO.7Usethedefinitionofcongruenceintermsofrigidmotionstoshowthattwotrianglesarecongruentifandonlyifcorrespondingpairsofsidesandcorrespondingpairsofanglesarecongruent.G.CO.8Explainhowthecriteriafortrianglecongruence(ASA,SAS,andSSS)followfromthedefinitionofcongruenceintermsofrigidmotions.

    G.CO.10Provetheoremsabouttriangles.

    Parts of a TriangleTheformedbythelegsiscalledthe____________________.Theothertwosinanisoscelesarecalled__________________.

    The3rdsideofthetriangleiscalledthe

    _______________.

    Isoscelestriangleshavetwocongruentsidescalledthe__________.

    Isosceles

    Iftwosidesofatrianglearecongruent,thentheanglesoppositethemarecongruent.

    ISOSCELES TRIANGLE THM

    IfABAC,thenB_______CONVERSE of ISOSCELES TRIANGLE THM

    Iftwoanglesofatrianglearecongruent,thenthesidesoppositethemarecongruent.IfBC,thenAB ______

  • 4.6isoscelesandequilateraltrianglesink.notebook

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    EquilateralEQUILATERAL COROLLARIES

    Atriangleisequilateralifandonlyifitis__________________.

    Eachangleofanequilateraltrianglemeasures______.

    F

    G

    H

    InFGH,FHGH.Nametwocongruentangles.

    a)

    b) 3m

    R

    S

    T

    3m

    3m

    FindthemeasuresofR,S,andT.

  • 4.6isoscelesandequilateraltrianglesink.notebook

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    c)

    d)

    F

    G

    H

    K J

    F

    G

    H

    K J

    IfFGKisequiangularandFG=15,then

    GK=______.

    ____________.

    IfFHFJ,then

    e) f) FindxFindx

  • 4.6isoscelesandequilateraltrianglesink.notebook

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    Findthevalueofthevariable.

    1. 2. FindxandmT.Findx,givenBCBA.

    Findthevalueofthevariable.3. Findxandy. 4.

  • 4.6isoscelesandequilateraltrianglesink.notebook

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    Findthevalueofthevariable.

    5. 6.

    EXTRA

  • 4.6isoscelesandequilateraltrianglesink.notebook

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    Provethatifalineisparalleltoonesideofanequilateraltriangle,thenitformsanotherequilateraltriangle.

    A.

    On the Worksheet

    PRACTICE

    Findthevalueofthevariablebywritinganequationandshowingallwork.

    1. 2.

  • 4.6isoscelesandequilateraltrianglesink.notebook

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    3. 4.2x

    A

    B

    C(6x+6)

    6.5.

    7. 8. 9.

  • 4.6isoscelesandequilateraltrianglesink.notebook

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    Refer to the figure at the right.

    10.

    11.

    12.IfEBAEAB,nametwocongruentsegments.

    13.IfCEDCDE,nametwocongruentsegments.

    Find each measure.

    14.mABC 15.mEDF

    Find each measure.

    16.mKML

    17.mHMG

    18.mGHM

    19.IfmHJM=145,findmMHJ

    20.IfmG=67,findmGHM

    mKMH=50 21.SPORTSApennantforthesportsteamsatLincolnHighSchoolisintheshapeofanisoscelestriangle.Ifthemeasureofthevertexangleis18,findthemeasureofeachbaseangle.

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    From the book:Find each measure.

    22.mBAC 23.mSRTFrom the book:

    Find each measure.

    25.CB24.TR

    Answers:

    1.4x+40=180,x=353.14x+12=180,x=12

    5.4x4=3x+8,x=127.2(2x+3)+90=180,x=21

    9.6x+12+90=180,x=1311.BECECB15.7017.7019.17.521.81and8123.6525.3

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